A. Introduction

When fluids flow at very low velocities, all the individual particles are flowing in parallel lines. This type of flow is called laminar flow. If a fluid stream enters a duct with a uniform velocity a velocity profile develops as the fluid moves down the tube, with the velocity at the duct wall being zero. At a sufficient distance downstream from the inlet, the velocity pattern becomes fixed. The shape of the velocity distribution curve is parabolic for flow in a tube or between parallel plates.

If the velocity of the fluid is gradually increased, there will be a point at which the fluid no longer flows in parallel lines, but by a series of eddies that result in a complete mixing of all parts of the flow except those immediately adjacent to the wall. This type of flow is called turbulent flow. The Reynolds number at which the flow changes from laminar to turbulent is the "critical Reynolds number" Re, where Re = u ρ d /η where u is the fluid average velocity, ρ its density, η its viscosity and d the channel equivalent diameter. The value of the critical Reynolds number in round tubes is between 2,100 and 2,300. In long rectangular ducts and annular spaces, the transition from laminar to turbulent flow also starts at a Reynolds number of 2,100 when the hydraulic diameter of the duct is used as the characteristic geometric dimension in calculating the Reynolds number.

At Reynolds numbers greater than 10⁴, the flow is fully turbulent. Between the lower and upper limits lies the zone of transition from laminar to turbulent flow. These limits are affected by the type of entry, initial disturbances in the fluid, roughness, and so on.

If the duct wall is at a temperature different from that of the fluid, heat will be transferred and a temperature profile will develop in the fluid. At a sufficient distance from the beginning of heating or cooling, the temperature profile becomes fully developed and therefore the heat transfer coefficient is constant. The rate of heat transfer is always greater in turbulent flow.